What is (\partial)/(\partial x)(-ysec^2(x)) ?

The answer to (\partial)/(\partial x)(-ysec^2(x)) is -2ysec^2(x)tan(x)

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(\partial)/(\partial x)(-ysec^2(x))

\frac{\partial}{\partial x} (- y sec^{2} (x))

- 2 y sec^{2} (x) tan (x)

Solution steps

\frac{\partial}{\partial x} (- y sec^{2} (x))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - y \frac{\partial}{\partial x} (sec^{2} (x))

Apply the chain rule:

2 sec (x) \frac{\partial}{\partial x} (sec (x))

= 2 sec (x) \frac{\partial}{\partial x} (sec (x))

\frac{\partial}{\partial x} (sec (x)) = sec (x) tan (x)

= - y \cdot 2 sec (x) sec (x) tan (x)

Simplify

- y \cdot 2 sec (x) sec (x) tan (x) : - 2 y sec^{2} (x) tan (x)

= - 2 y sec^{2} (x) tan (x)

What is (\partial)/(\partial x)(-ysec^2(x)) ?
The answer to (\partial)/(\partial x)(-ysec^2(x)) is -2ysec^2(x)tan(x)